yimingzhang/prime-factorization · Datasets at Hugging Face

input stringlengths 3 7	output stringlengths 3 41	step_by_step_solution listlengths 1 21
4520406	2 3 11 68491	[ "4520406 2 2260203", "2260203 3 753401", "753401 11 68491", "68491 68491 1" ]
405878	2 11 19 971	[ "405878 2 202939", "202939 11 18449", "18449 19 971", "971 971 1" ]
3668191	743 4937	[ "3668191 743 4937", "4937 4937 1" ]
2402284	2 2 19 73 433	[ "2402284 2 1201142", "1201142 2 600571", "600571 19 31609", "31609 73 433", "433 433 1" ]
1537269	3 107 4789	[ "1537269 3 512423", "512423 107 4789", "4789 4789 1" ]
1637014	2 59 13873	[ "1637014 2 818507", "818507 59 13873", "13873 13873 1" ]
4038549	3 1346183	[ "4038549 3 1346183", "1346183 1346183 1" ]
3280895	5 131 5009	[ "3280895 5 656179", "656179 131 5009", "5009 5009 1" ]
3939941	89 44269	[ "3939941 89 44269", "44269 44269 1" ]
3766005	3 3 5 83689	[ "3766005 3 1255335", "1255335 3 418445", "418445 5 83689", "83689 83689 1" ]
4515527	223 20249	[ "4515527 223 20249", "20249 20249 1" ]
1318824	2 2 2 3 3 13 1409	[ "1318824 2 659412", "659412 2 329706", "329706 2 164853", "164853 3 54951", "54951 3 18317", "18317 13 1409", "1409 1409 1" ]
3952558	2 109 18131	[ "3952558 2 1976279", "1976279 109 18131", "18131 18131 1" ]
2723880	2 2 2 3 5 22699	[ "2723880 2 1361940", "1361940 2 680970", "680970 2 340485", "340485 3 113495", "113495 5 22699", "22699 22699 1" ]
4989415	5 17 58699	[ "4989415 5 997883", "997883 17 58699", "58699 58699 1" ]
1672631	1672631	[ "1672631 1672631 1" ]
177943	177943	[ "177943 177943 1" ]
4315601	4315601	[ "4315601 4315601 1" ]
409332	2 2 3 7 11 443	[ "409332 2 204666", "204666 2 102333", "102333 3 34111", "34111 7 4873", "4873 11 443", "443 443 1" ]
593254	2 296627	[ "593254 2 296627", "296627 296627 1" ]
4976601	3 7 236981	[ "4976601 3 1658867", "1658867 7 236981", "236981 236981 1" ]
1297061	1297061	[ "1297061 1297061 1" ]
1575127	37 42571	[ "1575127 37 42571", "42571 42571 1" ]
4483431	3 3 3 3 55351	[ "4483431 3 1494477", "1494477 3 498159", "498159 3 166053", "166053 3 55351", "55351 55351 1" ]
916408	2 2 2 19 6029	[ "916408 2 458204", "458204 2 229102", "229102 2 114551", "114551 19 6029", "6029 6029 1" ]
756462	2 3 7 7 31 83	[ "756462 2 378231", "378231 3 126077", "126077 7 18011", "18011 7 2573", "2573 31 83", "83 83 1" ]
3416056	2 2 2 7 61001	[ "3416056 2 1708028", "1708028 2 854014", "854014 2 427007", "427007 7 61001", "61001 61001 1" ]
1932394	2 966197	[ "1932394 2 966197", "966197 966197 1" ]
2932205	5 139 4219	[ "2932205 5 586441", "586441 139 4219", "4219 4219 1" ]
3096956	2 2 774239	[ "3096956 2 1548478", "1548478 2 774239", "774239 774239 1" ]
2709825	3 5 5 36131	[ "2709825 3 903275", "903275 5 180655", "180655 5 36131", "36131 36131 1" ]
2233286	2 11 101513	[ "2233286 2 1116643", "1116643 11 101513", "101513 101513 1" ]
942113	942113	[ "942113 942113 1" ]
628424	2 2 2 78553	[ "628424 2 314212", "314212 2 157106", "157106 2 78553", "78553 78553 1" ]
706225	5 5 13 41 53	[ "706225 5 141245", "141245 5 28249", "28249 13 2173", "2173 41 53", "53 53 1" ]
3188777	83 103 373	[ "3188777 83 38419", "38419 103 373", "373 373 1" ]
1960909	1960909	[ "1960909 1960909 1" ]
3896855	5 31 31 811	[ "3896855 5 779371", "779371 31 25141", "25141 31 811", "811 811 1" ]
3419627	1721 1987	[ "3419627 1721 1987", "1987 1987 1" ]
1376146	2 688073	[ "1376146 2 688073", "688073 688073 1" ]
4975965	3 3 3 5 29 31 41	[ "4975965 3 1658655", "1658655 3 552885", "552885 3 184295", "184295 5 36859", "36859 29 1271", "1271 31 41", "41 41 1" ]
2798902	2 37 109 347	[ "2798902 2 1399451", "1399451 37 37823", "37823 109 347", "347 347 1" ]
182069	97 1877	[ "182069 97 1877", "1877 1877 1" ]
3826051	31 83 1487	[ "3826051 31 123421", "123421 83 1487", "1487 1487 1" ]
2549642	2 23 43 1289	[ "2549642 2 1274821", "1274821 23 55427", "55427 43 1289", "1289 1289 1" ]
724233	3 73 3307	[ "724233 3 241411", "241411 73 3307", "3307 3307 1" ]
4728061	13 367 991	[ "4728061 13 363697", "363697 367 991", "991 991 1" ]
1494816	2 2 2 2 2 3 23 677	[ "1494816 2 747408", "747408 2 373704", "373704 2 186852", "186852 2 93426", "93426 2 46713", "46713 3 15571", "15571 23 677", "677 677 1" ]
2779343	7 23 61 283	[ "2779343 7 397049", "397049 23 17263", "17263 61 283", "283 283 1" ]
2414166	2 3 402361	[ "2414166 2 1207083", "1207083 3 402361", "402361 402361 1" ]
527331	3 7 25111	[ "527331 3 175777", "175777 7 25111", "25111 25111 1" ]
4464948	2 2 3 17 43 509	[ "4464948 2 2232474", "2232474 2 1116237", "1116237 3 372079", "372079 17 21887", "21887 43 509", "509 509 1" ]
3216497	3216497	[ "3216497 3216497 1" ]
129741	3 59 733	[ "129741 3 43247", "43247 59 733", "733 733 1" ]
3115350	2 3 3 5 5 7 23 43	[ "3115350 2 1557675", "1557675 3 519225", "519225 3 173075", "173075 5 34615", "34615 5 6923", "6923 7 989", "989 23 43", "43 43 1" ]
1850297	17 31 3511	[ "1850297 17 108841", "108841 31 3511", "3511 3511 1" ]
2536634	2 317 4001	[ "2536634 2 1268317", "1268317 317 4001", "4001 4001 1" ]
2998921	2998921	[ "2998921 2998921 1" ]
3515124	2 2 3 17 17231	[ "3515124 2 1757562", "1757562 2 878781", "878781 3 292927", "292927 17 17231", "17231 17231 1" ]
4616054	2 23 23 4363	[ "4616054 2 2308027", "2308027 23 100349", "100349 23 4363", "4363 4363 1" ]
1939443	3 11 58771	[ "1939443 3 646481", "646481 11 58771", "58771 58771 1" ]
39959	31 1289	[ "39959 31 1289", "1289 1289 1" ]
2701043	47 101 569	[ "2701043 47 57469", "57469 101 569", "569 569 1" ]
1184545	5 236909	[ "1184545 5 236909", "236909 236909 1" ]
598091	13 13 3539	[ "598091 13 46007", "46007 13 3539", "3539 3539 1" ]
1910245	5 83 4603	[ "1910245 5 382049", "382049 83 4603", "4603 4603 1" ]
2957738	2 7 7 30181	[ "2957738 2 1478869", "1478869 7 211267", "211267 7 30181", "30181 30181 1" ]
4233096	2 2 2 3 3 7 37 227	[ "4233096 2 2116548", "2116548 2 1058274", "1058274 2 529137", "529137 3 176379", "176379 3 58793", "58793 7 8399", "8399 37 227", "227 227 1" ]
2043271	967 2113	[ "2043271 967 2113", "2113 2113 1" ]
177696	2 2 2 2 2 3 3 617	[ "177696 2 88848", "88848 2 44424", "44424 2 22212", "22212 2 11106", "11106 2 5553", "5553 3 1851", "1851 3 617", "617 617 1" ]
2655507	3 885169	[ "2655507 3 885169", "885169 885169 1" ]
1783989	3 3 198221	[ "1783989 3 594663", "594663 3 198221", "198221 198221 1" ]
2785822	2 13 109 983	[ "2785822 2 1392911", "1392911 13 107147", "107147 109 983", "983 983 1" ]
2114267	43 49169	[ "2114267 43 49169", "49169 49169 1" ]
3450234	2 3 43 43 311	[ "3450234 2 1725117", "1725117 3 575039", "575039 43 13373", "13373 43 311", "311 311 1" ]
4310706	2 3 23 31237	[ "4310706 2 2155353", "2155353 3 718451", "718451 23 31237", "31237 31237 1" ]
3812683	7 61 8929	[ "3812683 7 544669", "544669 61 8929", "8929 8929 1" ]
3922276	2 2 149 6581	[ "3922276 2 1961138", "1961138 2 980569", "980569 149 6581", "6581 6581 1" ]
565738	2 282869	[ "565738 2 282869", "282869 282869 1" ]
2989128	2 2 2 3 269 463	[ "2989128 2 1494564", "1494564 2 747282", "747282 2 373641", "373641 3 124547", "124547 269 463", "463 463 1" ]
661471	269 2459	[ "661471 269 2459", "2459 2459 1" ]
548071	29 18899	[ "548071 29 18899", "18899 18899 1" ]
2050607	13 157739	[ "2050607 13 157739", "157739 157739 1" ]
4040015	5 7 115429	[ "4040015 5 808003", "808003 7 115429", "115429 115429 1" ]
881234	2 499 883	[ "881234 2 440617", "440617 499 883", "883 883 1" ]
4846655	5 11 11 8011	[ "4846655 5 969331", "969331 11 88121", "88121 11 8011", "8011 8011 1" ]
1555244	2 2 293 1327	[ "1555244 2 777622", "777622 2 388811", "388811 293 1327", "1327 1327 1" ]
354008	2 2 2 17 19 137	[ "354008 2 177004", "177004 2 88502", "88502 2 44251", "44251 17 2603", "2603 19 137", "137 137 1" ]
4110036	2 2 3 7 113 433	[ "4110036 2 2055018", "2055018 2 1027509", "1027509 3 342503", "342503 7 48929", "48929 113 433", "433 433 1" ]
1146072	2 2 2 3 17 53 53	[ "1146072 2 573036", "573036 2 286518", "286518 2 143259", "143259 3 47753", "47753 17 2809", "2809 53 53", "53 53 1" ]
2215635	3 5 147709	[ "2215635 3 738545", "738545 5 147709", "147709 147709 1" ]
1279504	2 2 2 2 211 379	[ "1279504 2 639752", "639752 2 319876", "319876 2 159938", "159938 2 79969", "79969 211 379", "379 379 1" ]
2559228	2 2 3 7 30467	[ "2559228 2 1279614", "1279614 2 639807", "639807 3 213269", "213269 7 30467", "30467 30467 1" ]
258420	2 2 3 5 59 73	[ "258420 2 129210", "129210 2 64605", "64605 3 21535", "21535 5 4307", "4307 59 73", "73 73 1" ]
2620301	2620301	[ "2620301 2620301 1" ]
1756632	2 2 2 3 53 1381	[ "1756632 2 878316", "878316 2 439158", "439158 2 219579", "219579 3 73193", "73193 53 1381", "1381 1381 1" ]
2368387	7 338341	[ "2368387 7 338341", "338341 338341 1" ]
208430	2 5 19 1097	[ "208430 2 104215", "104215 5 20843", "20843 19 1097", "1097 1097 1" ]
2695376	2 2 2 2 29 37 157	[ "2695376 2 1347688", "1347688 2 673844", "673844 2 336922", "336922 2 168461", "168461 29 5809", "5809 37 157", "157 157 1" ]
918412	2 2 11 20873	[ "918412 2 459206", "459206 2 229603", "229603 11 20873", "20873 20873 1" ]

4520406

2 3 11 68491

[ "4520406 2 2260203", "2260203 3 753401", "753401 11 68491", "68491 68491 1" ]

405878

2 11 19 971

[ "405878 2 202939", "202939 11 18449", "18449 19 971", "971 971 1" ]

3668191

743 4937

[ "3668191 743 4937", "4937 4937 1" ]

2402284

2 2 19 73 433

[ "2402284 2 1201142", "1201142 2 600571", "600571 19 31609", "31609 73 433", "433 433 1" ]

1537269

3 107 4789

[ "1537269 3 512423", "512423 107 4789", "4789 4789 1" ]

1637014

2 59 13873

[ "1637014 2 818507", "818507 59 13873", "13873 13873 1" ]

4038549

3 1346183

[ "4038549 3 1346183", "1346183 1346183 1" ]

3280895

5 131 5009

[ "3280895 5 656179", "656179 131 5009", "5009 5009 1" ]

3939941

89 44269

[ "3939941 89 44269", "44269 44269 1" ]

3766005

3 3 5 83689

[ "3766005 3 1255335", "1255335 3 418445", "418445 5 83689", "83689 83689 1" ]

4515527

223 20249

[ "4515527 223 20249", "20249 20249 1" ]

1318824

2 2 2 3 3 13 1409

[ "1318824 2 659412", "659412 2 329706", "329706 2 164853", "164853 3 54951", "54951 3 18317", "18317 13 1409", "1409 1409 1" ]

3952558

2 109 18131

[ "3952558 2 1976279", "1976279 109 18131", "18131 18131 1" ]

2723880

2 2 2 3 5 22699

[ "2723880 2 1361940", "1361940 2 680970", "680970 2 340485", "340485 3 113495", "113495 5 22699", "22699 22699 1" ]

4989415

5 17 58699

[ "4989415 5 997883", "997883 17 58699", "58699 58699 1" ]

1672631

[ "1672631 1672631 1" ]

177943

[ "177943 177943 1" ]

4315601

[ "4315601 4315601 1" ]

409332

2 2 3 7 11 443

[ "409332 2 204666", "204666 2 102333", "102333 3 34111", "34111 7 4873", "4873 11 443", "443 443 1" ]

593254

2 296627

[ "593254 2 296627", "296627 296627 1" ]

4976601

3 7 236981

[ "4976601 3 1658867", "1658867 7 236981", "236981 236981 1" ]

1297061

[ "1297061 1297061 1" ]

1575127

37 42571

[ "1575127 37 42571", "42571 42571 1" ]

4483431

3 3 3 3 55351

[ "4483431 3 1494477", "1494477 3 498159", "498159 3 166053", "166053 3 55351", "55351 55351 1" ]

916408

2 2 2 19 6029

[ "916408 2 458204", "458204 2 229102", "229102 2 114551", "114551 19 6029", "6029 6029 1" ]

756462

2 3 7 7 31 83

[ "756462 2 378231", "378231 3 126077", "126077 7 18011", "18011 7 2573", "2573 31 83", "83 83 1" ]

3416056

2 2 2 7 61001

[ "3416056 2 1708028", "1708028 2 854014", "854014 2 427007", "427007 7 61001", "61001 61001 1" ]

1932394

2 966197

[ "1932394 2 966197", "966197 966197 1" ]

2932205

5 139 4219

[ "2932205 5 586441", "586441 139 4219", "4219 4219 1" ]

3096956

2 2 774239

[ "3096956 2 1548478", "1548478 2 774239", "774239 774239 1" ]

2709825

3 5 5 36131

[ "2709825 3 903275", "903275 5 180655", "180655 5 36131", "36131 36131 1" ]

2233286

2 11 101513

[ "2233286 2 1116643", "1116643 11 101513", "101513 101513 1" ]

942113

[ "942113 942113 1" ]

628424

2 2 2 78553

[ "628424 2 314212", "314212 2 157106", "157106 2 78553", "78553 78553 1" ]

706225

5 5 13 41 53

[ "706225 5 141245", "141245 5 28249", "28249 13 2173", "2173 41 53", "53 53 1" ]

3188777

83 103 373

[ "3188777 83 38419", "38419 103 373", "373 373 1" ]

1960909

[ "1960909 1960909 1" ]

3896855

5 31 31 811

[ "3896855 5 779371", "779371 31 25141", "25141 31 811", "811 811 1" ]

3419627

1721 1987

[ "3419627 1721 1987", "1987 1987 1" ]

1376146

2 688073

[ "1376146 2 688073", "688073 688073 1" ]

4975965

3 3 3 5 29 31 41

[ "4975965 3 1658655", "1658655 3 552885", "552885 3 184295", "184295 5 36859", "36859 29 1271", "1271 31 41", "41 41 1" ]

2798902

2 37 109 347

[ "2798902 2 1399451", "1399451 37 37823", "37823 109 347", "347 347 1" ]

182069

97 1877

[ "182069 97 1877", "1877 1877 1" ]

3826051

31 83 1487

[ "3826051 31 123421", "123421 83 1487", "1487 1487 1" ]

2549642

2 23 43 1289

[ "2549642 2 1274821", "1274821 23 55427", "55427 43 1289", "1289 1289 1" ]

724233

3 73 3307

[ "724233 3 241411", "241411 73 3307", "3307 3307 1" ]

4728061

13 367 991

[ "4728061 13 363697", "363697 367 991", "991 991 1" ]

1494816

2 2 2 2 2 3 23 677

[ "1494816 2 747408", "747408 2 373704", "373704 2 186852", "186852 2 93426", "93426 2 46713", "46713 3 15571", "15571 23 677", "677 677 1" ]

2779343

7 23 61 283

[ "2779343 7 397049", "397049 23 17263", "17263 61 283", "283 283 1" ]

2414166

2 3 402361

[ "2414166 2 1207083", "1207083 3 402361", "402361 402361 1" ]

527331

3 7 25111

[ "527331 3 175777", "175777 7 25111", "25111 25111 1" ]

4464948

2 2 3 17 43 509

[ "4464948 2 2232474", "2232474 2 1116237", "1116237 3 372079", "372079 17 21887", "21887 43 509", "509 509 1" ]

3216497

[ "3216497 3216497 1" ]

129741

3 59 733

[ "129741 3 43247", "43247 59 733", "733 733 1" ]

3115350

2 3 3 5 5 7 23 43

[ "3115350 2 1557675", "1557675 3 519225", "519225 3 173075", "173075 5 34615", "34615 5 6923", "6923 7 989", "989 23 43", "43 43 1" ]

1850297

17 31 3511

[ "1850297 17 108841", "108841 31 3511", "3511 3511 1" ]

2536634

2 317 4001

[ "2536634 2 1268317", "1268317 317 4001", "4001 4001 1" ]

2998921

[ "2998921 2998921 1" ]

3515124

2 2 3 17 17231

[ "3515124 2 1757562", "1757562 2 878781", "878781 3 292927", "292927 17 17231", "17231 17231 1" ]

4616054

2 23 23 4363

[ "4616054 2 2308027", "2308027 23 100349", "100349 23 4363", "4363 4363 1" ]

1939443

3 11 58771

[ "1939443 3 646481", "646481 11 58771", "58771 58771 1" ]

39959

31 1289

[ "39959 31 1289", "1289 1289 1" ]

2701043

47 101 569

[ "2701043 47 57469", "57469 101 569", "569 569 1" ]

1184545

5 236909

[ "1184545 5 236909", "236909 236909 1" ]

598091

13 13 3539

[ "598091 13 46007", "46007 13 3539", "3539 3539 1" ]

1910245

5 83 4603

[ "1910245 5 382049", "382049 83 4603", "4603 4603 1" ]

2957738

2 7 7 30181

[ "2957738 2 1478869", "1478869 7 211267", "211267 7 30181", "30181 30181 1" ]

4233096

2 2 2 3 3 7 37 227

[ "4233096 2 2116548", "2116548 2 1058274", "1058274 2 529137", "529137 3 176379", "176379 3 58793", "58793 7 8399", "8399 37 227", "227 227 1" ]

2043271

967 2113

[ "2043271 967 2113", "2113 2113 1" ]

177696

2 2 2 2 2 3 3 617

[ "177696 2 88848", "88848 2 44424", "44424 2 22212", "22212 2 11106", "11106 2 5553", "5553 3 1851", "1851 3 617", "617 617 1" ]

2655507

3 885169

[ "2655507 3 885169", "885169 885169 1" ]

1783989

3 3 198221

[ "1783989 3 594663", "594663 3 198221", "198221 198221 1" ]

2785822

2 13 109 983

[ "2785822 2 1392911", "1392911 13 107147", "107147 109 983", "983 983 1" ]

2114267

43 49169

[ "2114267 43 49169", "49169 49169 1" ]

3450234

2 3 43 43 311

[ "3450234 2 1725117", "1725117 3 575039", "575039 43 13373", "13373 43 311", "311 311 1" ]

4310706

2 3 23 31237

[ "4310706 2 2155353", "2155353 3 718451", "718451 23 31237", "31237 31237 1" ]

3812683

7 61 8929

[ "3812683 7 544669", "544669 61 8929", "8929 8929 1" ]

3922276

2 2 149 6581

[ "3922276 2 1961138", "1961138 2 980569", "980569 149 6581", "6581 6581 1" ]

565738

2 282869

[ "565738 2 282869", "282869 282869 1" ]

2989128

2 2 2 3 269 463

[ "2989128 2 1494564", "1494564 2 747282", "747282 2 373641", "373641 3 124547", "124547 269 463", "463 463 1" ]

661471

269 2459

[ "661471 269 2459", "2459 2459 1" ]

548071

29 18899

[ "548071 29 18899", "18899 18899 1" ]

2050607

13 157739

[ "2050607 13 157739", "157739 157739 1" ]

4040015

5 7 115429

[ "4040015 5 808003", "808003 7 115429", "115429 115429 1" ]

881234

2 499 883

[ "881234 2 440617", "440617 499 883", "883 883 1" ]

4846655

5 11 11 8011

[ "4846655 5 969331", "969331 11 88121", "88121 11 8011", "8011 8011 1" ]

1555244

2 2 293 1327

[ "1555244 2 777622", "777622 2 388811", "388811 293 1327", "1327 1327 1" ]

354008

2 2 2 17 19 137

[ "354008 2 177004", "177004 2 88502", "88502 2 44251", "44251 17 2603", "2603 19 137", "137 137 1" ]

4110036

2 2 3 7 113 433

[ "4110036 2 2055018", "2055018 2 1027509", "1027509 3 342503", "342503 7 48929", "48929 113 433", "433 433 1" ]

1146072

2 2 2 3 17 53 53

[ "1146072 2 573036", "573036 2 286518", "286518 2 143259", "143259 3 47753", "47753 17 2809", "2809 53 53", "53 53 1" ]

2215635

3 5 147709

[ "2215635 3 738545", "738545 5 147709", "147709 147709 1" ]

1279504

2 2 2 2 211 379

[ "1279504 2 639752", "639752 2 319876", "319876 2 159938", "159938 2 79969", "79969 211 379", "379 379 1" ]

2559228

2 2 3 7 30467

[ "2559228 2 1279614", "1279614 2 639807", "639807 3 213269", "213269 7 30467", "30467 30467 1" ]

258420

2 2 3 5 59 73

[ "258420 2 129210", "129210 2 64605", "64605 3 21535", "21535 5 4307", "4307 59 73", "73 73 1" ]

2620301

[ "2620301 2620301 1" ]

1756632

2 2 2 3 53 1381

[ "1756632 2 878316", "878316 2 439158", "439158 2 219579", "219579 3 73193", "73193 53 1381", "1381 1381 1" ]

2368387

7 338341

[ "2368387 7 338341", "338341 338341 1" ]

208430

2 5 19 1097

[ "208430 2 104215", "104215 5 20843", "20843 19 1097", "1097 1097 1" ]

2695376

2 2 2 2 29 37 157

[ "2695376 2 1347688", "1347688 2 673844", "673844 2 336922", "336922 2 168461", "168461 29 5809", "5809 37 157", "157 157 1" ]

918412

2 2 11 20873

[ "918412 2 459206", "459206 2 229603", "229603 11 20873", "20873 20873 1" ]